Here's Stripe using the term today - https://x.com/stevekaliski/status/2021034048945070360?s=20

And here's Google using the term to describe Jules - https://news.ycombinator.com/item?id=44813854

So fairly large players are using “async agent” to mean something specific, which seems enough to warrant defining it. It also makes sense that it’s far less common than “autonomous agent”, since “async” is mostly used by technical folks, which is a much smaller audience. I’m definitely in that sf/swe/tech/startup information bubble, but that's where this stuff is taking off.